How SpaceX is able to achieve its amazing rocket landing accuracy

After SpaceX’s successful and uniquely exciting launch of Taiwan’s Formosat-5 remote sensing satellite, Elon Musk took to Twitter to reveal some fascinating details about the launch and recovery of the Falcon 9 first stage.

Unabashedly technical, the details Musk revealed demonstrate the truly incredible accuracy of Falcon 9’s recovery, honed over 20 landing attempts and numerous modifications to the launch vehicle. The accuracy is best understood within the context of Falcon 9’s scale and the general scope of orbital rocketry.

The first stage of Falcon 9 Full Thrust, currently the active version of Falcon 9, stands 140 feet tall and 12 feet in diameter. If you can, for a moment, picture a 737 airliner, the plane most people have likely flown aboard on domestic flights. The first stage of Falcon 9 is the same length or greater and the same diameter as Boeing’s workhorse airliner. If you are now imagining a 737 landing on its tail aboard an ocean-going barge, that is a great start. The most common version of the 737, the -800, has an empty weight of 91,000 lb, while Falcon 9’s empty first stage is a bit more than half as heavy. With a full load of fuel, Falcon 9 S1 (first stage) weighs nearly three times as much as the 737-800. A single Merlin 1D engine out of Falcon 9’s namesake nine rocket engines has nearly ten times the thrust of the airliner. In short, Falcon 9’s first stage is massive, both extremely light and extremely heavy, and has a mind-boggling amount of thrust.

Falcon 9’s ability to land as accurately as it does is due to a combination of multiple technologies and vehicle modifications. Most visible are S1’s cold gas maneuvering thrusters and aluminum or titanium grid fins, both of which are designed to provide some level of control authority and maneuverability to the first stage during its trip within and without Earth’s atmosphere. At the peak of its trips, the first stage is often completely outside of the vast majority of the atmosphere, meaning that aerodynamic forces are no longer relevant or useful for the vehicle. This is where the cold gas thrusters come in: by carrying their reaction mass with them (the gas), Falcon 9 can maneuver outside of the atmosphere. Once the stage descends into thicker atmospheric conditions, the grid fins deploy and are used like wings to guide the stage down to its landing location, be that on land or at sea. While the gas thrusters lose a lot of their utility once in the atmosphere, they can still be used to add a small amount of control authority when needed. They were famously seen fighting a futile battle to save a first stage aboard OCISLY in 2015.

With this in mind, we can take a closer look at Musk’s technical details. First off, we have a photo of the landed booster, Falcon 9 1038, clearly almost dead center on the droneship Just Read The Instructions. More specifically, Musk reports that 1038 landed less than a single meter off the center of the target, and it landed with less than a single meter per second of latent velocity. The first stage thus managed both a soft and deadly accurate landing after traveling to a height of 150 miles – well into what is technically “space” – at a maximum speed of 1.5 miles per second. Without delving further into the details, this is best summarized as “insanely fast”, and is a bit faster than the X-15 rocketplane’s fastest recorded speed. To better put this into context, Falcon 9 1038 traveled to an altitude of 240,000 meters at a top speed of 2,400 meters per second, turned around, and landed on an autonomous barge about two feet off of its optimal target. It is truly difficult to describe how impressive that kind of accuracy is.

The hypersonic X-15 and Falcon 9 S1, with a 737-800 on the right. All vehicles are to scale. (Wikipedia, SpaceX)

Mr. Musk nevertheless did not let 1038 steal all the fanfare, and revealed that the first stage responsible for launching BulgariaSat-1, 1029, had the honor of being the fastest first stage yet, clocking in at at a truly staggering Mach 7.9, or 2,700 meters per second. That speedy mission marked the stage’s second flight and was SpaceX’s second successful reuse of a Falcon 9. Indicative of the intense speed and heat the core experienced, one of the vehicle’s grid fins was noted to have almost completely melted through. Aluminum’s melting point begins at 1,221°F.

The central aluminum grid fin of 1029 features a dramatic lack of several vanes, likely melted off during the intense heat of reentry. (Reddit, u/thedubya22)

SpaceX will move to titanium grid fins in the future, first trialed during 1036’s launch of Iridium-2. (SpaceX)

Never answered how the first stages are able to accurately land at the targeted locations though. At least that I saw.

It's actually a lot simpler than it looks, the math behind Control Theory is pretty groovy, but the principles are simple. All machine control works the same way, be it airplane autopilot, CNC machine or a rocket. In simple system, you measure the real situation, you know what the desired target situation looks like, difference of the two is the current error and you strive to drive the error towards zero. That works nicely for launching a rocket, you know where you are, you know where you want to go and thus you calculate what direction you need to go to. Landing a rocket is a bit more tricky, but there is a simple workaround. Math works the same no matter if you run your model forwards or backwards in time. If you want to land on target, what you need to do, is continually model how you would launch from target to your current location and just drive your control system to stay on that trajectory just with time reversed. How accurately you will be able to land depends on how accurately you can measure your location, how often you can recalculate your trajectory and how fast you can actuate your controls.With that approach you can do stuff like this: People think that controlling the rocket is hardest part about landing it, its not, they did vertical landings on Moon even before Apollo missions, the principles are similar, its really not as sci-fi as it looks.Hardest part is having a rocket that is mechanically capable of it to start with, nobody else but SpaceX has one like it. They took reuse into account when they set down the basic design of Falcon 9 in the first place. If they haven't done that they could never have pulled it off.